How can I use topographic maps?
An overview of topographic maps and
associated topics
Topographic maps as a way to visualize the surface of the
Earth
Topographic maps show the three-dimensional shape of the landscape by representing equal
elevation with lines on a two-dimensional map; they are in essence a type of contour map (also
used in meteorology and oceanography). Although these can be mathematically derived, most
geologists create them by measuring the elevation (and position) in the field (or on an aerial
photo), plotting elevation on a map and connecting lines of equal elevation (much like connectthe-dots except that all the same numbers are connected, rather than in sequence). This module is
designed to give you experience examining and reading topographic maps, understanding scale,
calculating slope and drawing topographic profiles.
Why should I become familiar with all aspects of
topographic maps?
Topographic maps will be familiar to those of you who are hikers or outdoor enthusiasts; they
are used to understand the landscape over which you will hike (or rock climb or ski, etc). They
are also commonly used by field geologists for a variety of applications. The ability to read and
interpret topographic maps is considered a basic skill for all geoscientists and geoscience
students. Topographic maps are used to understand the shape of the land, whether a slope will
fail, how glaciers are changing, and geologic history, among many other things. Geoscientists
make and use them to construct geologic maps, to find the best building sites, to estimate where
flooding will take place, and to determine the best sites for archeological or paleontological digs.
Parts of this module teach you about how to read topographic maps so that you can complete
other applications that these types of contour maps are used for.
Students of the geosciences who want to become proficient in reading topographic maps must
also learn about scale - the relation of the size of the map to the size of the area in real life. Why
should you care what the scale of the map is? The scale helps you understand how far you'll
have to hike to get to that lake, or the distance between two points on a road. Parts of this module
will take you through the types of scales, how to determine scale, and the standard types of
scales for topographic maps.
One of the most practical exercises found in geoscience textbooks involves calculating the slope
of a hillside or other part of the ground surface. Why would you want to calculate the slope of
a hillside? The slope can tell us whether this is a good site to build, whether a road will become
covered with debris, or how difficult it will be to hike to that peak. It also influences volcanic
hazards, limits permissible land use (such as farming and development), and much more. Parts of
this module will walk you through how to calculate the slope of a hillside or groundwater table
surface or anything for which you know the distance and difference in elevation.
Drawing a topographic profile is related to slope and understanding the shape of the land. Why
would you want to draw a profile of the landscape? Many geoscientists like to visualize the
shape of the land as if they had sliced through it. This helps them to see hazards, draw
conclusions about the strike and dip of the geology beneath the land, among other applications.
Parts of this module will walk you through the steps to making a topographic profile, something
geoscientists do often.
How do I calculate slope/gradient?
"Rise over run" in the geosciences
Many of us know that the slope of a line is
calculated by "rise over run". However, the application of slope calculation can seem a little
more complicated. In the geosciences, you may be asked to calculate the slope of a hill or to
determine rate by calculating the slope of a line on a graph. This page is designed to help you
learn these skills so that you can use them in your geoscience courses.
Why should I calculate slope or gradient?
In the geosciences slope can play an important role in a number of problems. The slope of a hill
can help to determine the amount of erosion likely during a rainstorm. The gradient of the water
table can help us to understand whether (and how much) contamination might affect a local well
or water source.
How do I calculate slope (or gradient) in the geosciences?
Gradient in the case of hillslope and water table is just like calculating the slope of a line on a
graph - "rise" over "run". But how do you do that using a contour (or topographic) map?
1. First get comfortable with the features of the topographic map of interest. Make sure you
know a few things:
o What is the contour interval (sometimes abbreviated CI)?
o What is the scale of the map?
o What is the feature for which you want to know the slope?
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Below there is a topographic map of Math State Park. You are interested in building a
path from the top of the hill on this map to the creek (Equation Creek) and want to know
the slope of the hill. You should probably print out the map (with the steps for
calculating slope) (Acrobat (PDF) 93kB Oct15 08).
.
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o
What is the contour interval of this map?
The contour interval tells you "rise", specifically the change in elevation between
each of the "brown lines" (contours). In this case, the contour interval is in the
key in the lower right and is abbreviated CI. The contour interval is 20 ft.
o What is the scale of the map?
The scale tells you the "run", or the distance on the ground. On this map, it is also
shown in the lower right and is shown only graphically. If you print out the map
(with the steps for calculating slope) (Acrobat (PDF) 93kB Oct15 08), you will
find that 1 inch = 1 mile.
o What is the feature for which you want to know the slope?
In this case, you want to know the slope of the hillside to the WNW from the top
(at 869 ft) to the creek.
2. First, you need to know "rise" for the feature. "Rise" is the difference in elevation from
the top to bottom (see the image above). So determine the elevation of the top of the hill
(or slope, or water table).
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The top of the hill of interest is 859 ft. The contour line at the creek where your path will
end is one below 700 ft. That makes it 680 ft (because the contour interval is 20 ft). The
difference in elevation is the top minus the bottom (859 ft - 680 ft) so "rise" = 179 ft
3. Next you need to know "run" for the feature. "Run" is the horizontal distance from the
highest elevation to the lowest. So, get out your ruler and measure that distance. If you
know the scale, you can calculate the distance. Most of the time distance on maps is
given in km or mi.
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The red line represents the distance along the hillslope where you want to build your
path. The red line is twice as long as the scale for one mile (on the printed map, it is about
2 inches). Thus, the distance from the top to bottom of the hill or "run" = 2 mi
4. Now comes the rise over run part. There are two ways that you may be asked to make
calculations relating to slope. Make sure you know what the question is asking you and
follow the steps associated with the appropriate process:
o If you are asked to calculate slope (as in a line or a hillside), a simple division is
all that is needed. Just make sure that you keep track of units!
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1. As we've seen throughout this page, slope is "rise over run". The phrase
"rise over run" implies that you will need to divide. The equation for slope
looks like this:
2. Take the difference in elevation and divide it by the horizontal difference
(always making sure you keep track of units).
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On the map of Math State Park the hill's rise = 179 ft and run is 2 mi. So
we set up the problem like this:
3. Finish the calculation using your calculator (or doing the calculations by
hand).
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Now we just divide the rise by the run and wind up with:
The units you end up with might be feet/mile or m/km or feet/foot (slope
can be expressed in all these ways). It just depends on what you started
with.
o
You may also be asked to calculate percent (or %) slope. This calculation takes
a couple of steps. And it mostly has to do with paying attention to units. The units
on both rise and run have to be the same.
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1. To calculate percent slope, both rise and run must be in the same
units(for example, feet or meters). If your horizontal distance is in miles,
you need to convert to feet; if the horizontal distance is in kilometers,
you'll have to convert to meters. (To convert from miles to feet, multiply
by 5280 ft/mi; km to m, multiply by 1000m/km. If you need more help
with this or need to convert other units, please see the unit conversions
module).
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Right now you have rise in feet and run in miles. Let's convert the miles to
feet by multiplying by the appropriate conversion factor: 1 mile = 5280
feet. So, we should multiply "run" by
:
2. Once you have converted so that both elevation and distance have the
same units, we can write an equation for slope: rise over run (implying rise
divided by run).
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We know that rise is 179 ft and run is 10560 ft:
But, hold on, there's one more step to getting to % slope.
3. To get to % we need to multiply the calculated slope (which is unitless
because the units cancel on the top and bottom) by 100 so that our
equation looks like this:
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Start with rise over run and multiply by 100:
4. Now plug in your numbers and calculate % slope!
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Note that % slope does not have any units because ft cancel in the
calculation. Make sure that you indicate that it's % however!